Controlling the breakup of spiral waves in an excitable medium by applying time-delay feedback signals

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

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SPATIOTEMPORAL IRREGULARITY IN A TWO-DIMENSIONAL MODEL OF CARDIAC TISSUE

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127491000142 ◽

1991 ◽

Vol 01 (01) ◽

pp. 219-225 ◽

Cited By ~ 57

Author(s):

A. V. PANFILOV ◽

A. V. HOLDEN

Keyword(s):

Cardiac Tissue ◽

Numerical Solutions ◽

Spiral Waves ◽

Excitable Medium ◽

Two Dimensional ◽

Dimensional Model ◽

Two Dimensional Model ◽

Solutions Of Equations

Meandering spiral waves are well-known solutions of equations that represent a two-dimensional excitable medium. Numerical solutions of a model for a sheet of cardiac tissue show transient meandering vortices that break down spontaneously into spatiotemporal irregularity.

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Pattern selection in neuronal network driven by electric autapses with diversity in time delays

International Journal of Modern Physics B ◽

10.1142/s0217979214502397 ◽

2014 ◽

Vol 29 (01) ◽

pp. 1450239 ◽

Cited By ~ 105

Author(s):

Jun Ma ◽

Huxin Qin ◽

Xinlin Song ◽

Runtong Chu

Keyword(s):

Time Delay ◽

Traveling Wave ◽

Time Delays ◽

Electric Activity ◽

Local Area ◽

Spiral Waves ◽

Collective Behaviors ◽

Numerical Studies ◽

Local Areas ◽

Delay Diversity

The electric activity of neuron and collective behaviors of neurons can be modulated by autapse, which can be described by self-feedback current in close loop with time delay being considered. Distribution of electric autapses in a local area can introduce heterogeneity in the network and thus traveling wave emits from this area. In this paper, diversity in time delay of electric autapse is considered and collision between emitting waves from different local areas driven by electric autapses under different time delays is observed. In the numerical studies, neurons in the square area with 15×15 (and/or 20×20) nodes are connected electric autapses with different time delays and target-like waves are induced and converted into, spiral waves after continuous collision between wave fronts. It is found that a group of spiral waves can emerge in the network, or coexist with target waves under appropriate coupling intensity due to time delay diversity in autapse and these waves can regulate the collective behaviors of neurons as continuous pacemakers.

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